{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fourier sine series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the sine functions $\\sin(n\\pi x)$ for $n=1,2,\\ldots$ on the interval $x \\in [0,1]$, with the \"usual\" function inner product $f(x) \\cdot g(x) = \\int_0^1 f(x) g(x) \\, dx$.  It is a remarkable fact that the sine functions are **orthogonal** under this dot product:\n",
    "\n",
    "$$\n",
    "\\sin(m\\pi x) \\cdot \\sin(n\\pi x) = \\int_0^1 \\sin(m\\pi x) \\sin(n\\pi x) \\, dx = \\begin{cases} 0 & m \\ne n \\\\ \\frac{1}{2} & m = n \\end{cases} .\n",
    "$$\n",
    "\n",
    "This can be verified by simply doing the integral, a first-year calculus exercise.  (The identity $\\sin A \\sin B = \\frac{1}{2}[\\cos (A-B) - \\cos(A+B)]$ is useful here.)\n",
    "\n",
    "Let's plot a few of these functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1.0, 'orthogonal sine functions')"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PyPlot\n",
    "x = range(0,1,length=100)\n",
    "plot(x, sin.(π*x), \"-\")\n",
    "plot(x, sin.(2π*x), \"-\")\n",
    "plot(x, sin.(3π*x), \"-\")\n",
    "plot(x, sin.(4π*x), \"-\")\n",
    "legend([L\"\\sin(\\pi x)\", L\"\\sin(2\\pi x)\", L\"\\sin(3\\pi x)\", L\"\\sin(4\\pi x)\"])\n",
    "xlabel(L\"x\")\n",
    "title(\"orthogonal sine functions\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sines as an orthogonal basis\n",
    "\n",
    "We can consider the $\\sin(n\\pi x)$ functions as an orthogonal basis for some set of functions, defined by all linear combinations of these $\\sin(n\\pi x)$ functions (their **span**).  At first glance, it seems like this should be a rather \"small\" subspace of all functions.  One of the most remarkable facts of mathematics, however, is that the span of the sine functions contains nearly all possible functions of practical interest!  This was first proposed by Fourier in 1807, but took almost 150 years to make rigorous and precise.\n",
    "\n",
    "For a function $f(x)$ defined on $x \\in [0,1]$, the [Fourier sine series](http://en.wikipedia.org/wiki/Fourier_sine_and_cosine_series) writes $f(x)$ as:\n",
    "$$\n",
    "f(x) = \\sum_{n=1}^\\infty b_n \\sin(n\\pi x)\n",
    "$$\n",
    "where the coefficients $b_n$ can be found by integration:\n",
    "$$\n",
    "b_m = 2 \\int_0^1 f(x) \\sin(m\\pi x) dx \\, .\n",
    "$$\n",
    "\n",
    "Let's define a function `sinecoef` in [Julia](http://julialang.org) to compute these [integrals numerically](http://en.wikipedia.org/wiki/Numerical_integration), using Julia's [quadgk](https://github.com/JuliaMath/QuadGK.jl) function  We'll use the `abstol` parameter to set an integration tolerance: we want the error to be small compared to $\\sqrt{\\int_0^1 |f(x)|^2 dx}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sinecoef (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pkg.add(\"QuadGK\") # uncomment to install QuadGK if needed.\n",
    "using QuadGK\n",
    "\n",
    "sinecoef(f, m) = 2 * quadgk(x -> f(x) * sin(m*π*x), 0,1, atol=1e-8 * sqrt(quadgk(x->abs2(f(x)),0,1)[1]))[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Truncated series = Projection = Fitting!\n",
    "\n",
    "In practice, of course, we are usually forced to truncate the series to a finite number N of terms:\n",
    "\n",
    "$$\n",
    "f(x) \\approx \\sum_{n=1}^N b_n \\sin(n\\pi x)\n",
    "$$\n",
    "\n",
    "while still computing $b_m = 2 \\int_0^1 f(x) \\sin(m\\pi x) dx$ as above.  The key thing to understand is that **this is orthogonal projection** of $f(x)$ onto the **N-dimensional subspace** spanned by $\\{\\sin(\\pi x), \\sin(2\\pi x), \\ldots, \\sin(N\\pi x)\\}$.\n",
    "\n",
    "And, just for projection with vectors in $\\mathbb{R}^m$, **projection is equivalent to least-square fitting**.  That means that truncating the Fourier series is equivalent to finding the $b_n$ that **minimize**\n",
    "$$\n",
    "\\left\\Vert f(x) - \\sum_{n=1}^N b_n \\sin(n\\pi x) \\right\\Vert^2 = \\int_0^1 \\left| f(x) - \\sum_{n=1}^N b_n \\sin(n\\pi x) \\right|^2 dx\n",
    "$$\n",
    "over all possible $\\{b_1,\\ldots,b_N\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A sine-series example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, if we have the function $f(x) = 0.5 - |x - 0.5|$, the first 20 coefficients are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20-element Array{Float64,1}:\n",
       "  0.4052847345693511\n",
       "  5.031872079333402e-18\n",
       " -0.045031637174372426\n",
       "  1.821156848822449e-17\n",
       "  0.016211389382773993\n",
       " -2.0848986065940786e-17\n",
       " -0.008271117032027663\n",
       " -1.2554430899086627e-17\n",
       "  0.005003515241596977\n",
       "  4.703324618594227e-17\n",
       " -0.0033494606162756263\n",
       " -7.308916560896717e-18\n",
       "  0.0023981345240789223\n",
       " -2.3414712309558446e-16\n",
       " -0.0018012654869748413\n",
       " -8.725341965181291e-17\n",
       "  0.0014023693237693808\n",
       "  3.6769709280601687e-16\n",
       " -0.0011226723949289694\n",
       " -4.114118967289368e-16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = 0.5 - abs(x - 0.5)\n",
    "sinecoef.(f, 1:20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(Notice that $b_n = 0$ for *even* $n$, which correspond to *antisymmetric* sine functions that integrate to zero against this *symmetric* $f$.)   The coefficients seem to be converging (getting smaller), as we would hope for a convergent series.  Let's plot them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x7fd9752b9b38>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PyPlot\n",
    "n = 1:2:99 # odd integers from 1 to 99\n",
    "loglog(n, abs.(sinecoef.(f, n)), \"bo\")\n",
    "xlabel(L\"n\")\n",
    "ylabel(L\"Fourier sine coefficient $|b_n|$\")\n",
    "title(L\"Sine series convergence for $f(x) = 0.5 - |x - 0.5|$\")\n",
    "loglog(n, 1 ./ n.^2, \"b--\")\n",
    "legend([L\"|b_n|\", L\"1/n^2\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They decay asymptotically as $1/n^2$.  It turns out that one can prove this from the fact that $f(x)$ is continuous with a discontinuous slope.\n",
    "\n",
    "Now let's plot the series itself and compare it to $f(x)$.  We'll use Julia's [Interact package](https://github.com/JuliaLang/Interact.jl) so that we can drag a slider to control the number of terms in the series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sinesum (generic function with 1 method)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First, define a function to evaluate N terms of the sine series, given the coefficients b\n",
    "function sinesum(b, x)\n",
    "    f = 0.0\n",
    "    for n = 1:length(b)\n",
    "        f += b[n] * sin(n*π*x)\n",
    "    end\n",
    "    return f\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script>\n",
       "// Immediately-invoked-function-expression to avoid global variables.\n",
       "(function() {\n",
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       "            window,\n",
       "        );\n",
       "    } else {\n",
       "        document\n",
       "            .querySelector('[data-webio-mountpoint=\"16406915794507829046\"]')\n",
       "            .innerHTML = (\n",
       "                '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb\">' +\n",
       "                '<p><strong>WebIO not detected.</strong></p>' +\n",
       "                '<p>Please read ' +\n",
       "                '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
       "                'for more information on how to resolve this issue.</p>' +\n",
       "                '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
       "                '</div>'\n",
       "            );\n",
       "    }\n",
       "    </script>\n",
       "</div>\n"
      ],
      "text/plain": [
       "Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Scope(Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :label), Any[\"n\"], Dict{Symbol,Any}(:className => \"interact \",:style => Dict{Any,Any}(:padding => \"5px 10px 0px 10px\")))], Dict{Symbol,Any}(:className => \"interact-flex-row-left\")), Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :input), Any[], Dict{Symbol,Any}(:max => 50,:min => 1,:attributes => Dict{Any,Any}(:type => \"range\",Symbol(\"data-bind\") => \"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\",\"orient\" => \"horizontal\"),:step => 1,:className => \"slider slider is-fullwidth\",:style => Dict{Any,Any}()))], Dict{Symbol,Any}(:className => \"interact-flex-row-center\")), Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :p), Any[], Dict{Symbol,Any}(:attributes => Dict(\"data-bind\" => \"text: formatted_val\")))], Dict{Symbol,Any}(:className => \"interact-flex-row-right\"))], Dict{Symbol,Any}(:className => \"interact-flex-row interact-widget\")), Dict{String,Tuple{Observables.AbstractObservable,Union{Nothing, Bool}}}(\"changes\" => (Observable{Int64} with 1 listeners. Value:\n",
       "0, nothing),\"index\" => (Observable{Any} with 2 listeners. Value:\n",
       "25, nothing)), Set{String}(), nothing, Asset[Asset(\"js\", \"knockout\", \"/home/vili/.julia/packages/Knockout/IP1uR/src/../assets/knockout.js\"), Asset(\"js\", \"knockout_punches\", \"/home/vili/.julia/packages/Knockout/IP1uR/src/../assets/knockout_punches.js\"), Asset(\"js\", nothing, \"/home/vili/.julia/packages/InteractBase/Zfu5P/src/../assets/all.js\"), Asset(\"css\", nothing, \"/home/vili/.julia/packages/InteractBase/Zfu5P/src/../assets/style.css\"), Asset(\"css\", nothing, \"/home/vili/.julia/packages/Interact/SbgIk/src/../assets/bulma_confined.min.css\")], Dict{Any,Any}(\"changes\" => Any[WebIO.JSString(\"(function (val){return (val!=this.model[\\\"changes\\\"]()) ? (this.valueFromJulia[\\\"changes\\\"]=true, this.model[\\\"changes\\\"](val)) : undefined})\")],\"index\" => Any[WebIO.JSString(\"(function (val){return (val!=this.model[\\\"index\\\"]()) ? (this.valueFromJulia[\\\"index\\\"]=true, this.model[\\\"index\\\"](val)) : undefined})\")]), WebIO.ConnectionPool(Channel{Any}(sz_max:32,sz_curr:0), Set{AbstractConnection}(), Base.GenericCondition{Base.AlwaysLockedST}(Base.InvasiveLinkedList{Task}(Task (runnable) @0x00007fd979757820, Task (runnable) @0x00007fd979757820), Base.AlwaysLockedST(1))), WebIO.JSString[WebIO.JSString(\"function () {\\n    var handler = (function (ko, koPunches) {\\n    ko.punches.enableAll();\\n    ko.bindingHandlers.numericValue = {\\n        init: function(element, valueAccessor, allBindings, data, context) {\\n            var stringified = ko.observable(ko.unwrap(valueAccessor()));\\n            stringified.subscribe(function(value) {\\n                var val = parseFloat(value);\\n                if (!isNaN(val)) {\\n                    valueAccessor()(val);\\n                }\\n            });\\n            valueAccessor().subscribe(function(value) {\\n                var str = JSON.stringify(value);\\n                if ((str == \\\"0\\\") && ([\\\"-0\\\", \\\"-0.\\\"].indexOf(stringified()) >= 0))\\n                     return;\\n                 if ([\\\"null\\\", \\\"\\\"].indexOf(str) >= 0)\\n                     return;\\n                stringified(str);\\n            });\\n            ko.applyBindingsToNode(\\n                element,\\n                {\\n                    value: stringified,\\n                    valueUpdate: allBindings.get('valueUpdate'),\\n                },\\n                context,\\n            );\\n        }\\n    };\\n    var json_data = {\\\"formatted_vals\\\":[\\\"1\\\",\\\"3\\\",\\\"5\\\",\\\"7\\\",\\\"9\\\",\\\"11\\\",\\\"13\\\",\\\"15\\\",\\\"17\\\",\\\"19\\\",\\\"21\\\",\\\"23\\\",\\\"25\\\",\\\"27\\\",\\\"29\\\",\\\"31\\\",\\\"33\\\",\\\"35\\\",\\\"37\\\",\\\"39\\\",\\\"41\\\",\\\"43\\\",\\\"45\\\",\\\"47\\\",\\\"49\\\",\\\"51\\\",\\\"53\\\",\\\"55\\\",\\\"57\\\",\\\"59\\\",\\\"61\\\",\\\"63\\\",\\\"65\\\",\\\"67\\\",\\\"69\\\",\\\"71\\\",\\\"73\\\",\\\"75\\\",\\\"77\\\",\\\"79\\\",\\\"81\\\",\\\"83\\\",\\\"85\\\",\\\"87\\\",\\\"89\\\",\\\"91\\\",\\\"93\\\",\\\"95\\\",\\\"97\\\",\\\"99\\\"],\\\"changes\\\":WebIO.getval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"8290815864971628922\\\",\\\"id\\\":\\\"5643236849644283174\\\",\\\"type\\\":\\\"observable\\\"}),\\\"index\\\":WebIO.getval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"8290815864971628922\\\",\\\"id\\\":\\\"2918820201965447682\\\",\\\"type\\\":\\\"observable\\\"})};\\n    var self = this;\\n    function AppViewModel() {\\n        for (var key in json_data) {\\n            var el = json_data[key];\\n            this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n        }\\n        \\n        [this[\\\"formatted_val\\\"]=ko.computed(    function(){\\n        return this.formatted_vals()[parseInt(this.index())-(1)];\\n    }\\n,this)]\\n        [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? 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       "Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Figure(PyObject <Figure size 640x480 with 1 Axes>)], Dict{Symbol,Any}(:className => \"interact-flex-row interact-widget\"))], Dict{Symbol,Any}())"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "@webio": {
       "kernelId": "1d906ee0-9117-4cf7-bb86-e93666d2a1a9"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Interact\n",
    "fig = figure()\n",
    "x = range(0,1, length=1000)\n",
    "@manipulate for n=1:2:99\n",
    "    withfig(fig) do\n",
    "        plot(x, f.(x), \"k--\")\n",
    "        b = sinecoef.(f, 1:n)\n",
    "        plot(x, [sinesum(b, x) for x in x], \"r-\")\n",
    "        xlabel(L\"$x$\")\n",
    "        legend([\"exact f\", \"$n-term sine series\"])\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In contrast, if we make a smoother function, e.g. $g(x) = \\sin(\\sin(3 \\pi x) + 5\\sin(\\pi x))$, then it eventually converges *much* more quickly (in fact, for a smooth function like this the series converges *exponentially* fast):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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       "            window,\n",
       "        );\n",
       "    } else {\n",
       "        document\n",
       "            .querySelector('[data-webio-mountpoint=\"18193625718085404310\"]')\n",
       "            .innerHTML = (\n",
       "                '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb\">' +\n",
       "                '<p><strong>WebIO not detected.</strong></p>' +\n",
       "                '<p>Please read ' +\n",
       "                '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
       "                'for more information on how to resolve this issue.</p>' +\n",
       "                '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
       "                '</div>'\n",
       "            );\n",
       "    }\n",
       "    </script>\n",
       "</div>\n"
      ],
      "text/plain": [
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      ]
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      }
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     "output_type": "execute_result"
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   ],
   "source": [
    "using Interact\n",
    "fig = figure(figsize=(15,6))\n",
    "g(x) = sin(sin(3π*x) + 5*sin(π*x))\n",
    "@manipulate for n=1:2:37\n",
    "    withfig(fig) do\n",
    "        fig.set_size_inches(15, 6)\n",
    "        subplot(1,2,1)\n",
    "        plot(x, g.(x), \"k--\")\n",
    "        b = sinecoef.(g, 1:n)\n",
    "        plot(x, [sinesum(b, x) for x in x], \"r-\")\n",
    "        xlabel(L\"x\")\n",
    "        legend([\"exact g\", \"$n-term sine series\"])\n",
    "        \n",
    "        subplot(1,2,2)\n",
    "        semilogy(1:2:n, abs.(b[1:2:n]), \"bo-\")\n",
    "        xlabel(L\"n\")\n",
    "        ylabel(L\"coefficient $|b_n|$\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Supplementary material\n",
    "\n",
    "The following material goes a bit beyond 18.06 (see e.g. 18.303), but it is provided as a supplement.\n",
    "\n",
    "## Solving the heat/diffusion equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have the heat equation $\\frac{\\partial^2 u}{\\partial x^2} = \\frac{\\partial u}{\\partial t}$, with Dirichlet boundary conditions $u(0,t) = u(1,t) = 0$, and initial condition $u(x,0) = f(x)$, we can solve the equation by expanding $u(x,t)$ in a Fourier sine series.  From class:\n",
    "\n",
    "* $u(x,t) = \\sum_{n=0}^\\infty b_n \\sin(n\\pi x) e^{-(n\\pi)^2 t}$\n",
    "\n",
    "where $b_n$ are the sine-series coefficients of the initial condition $f(x)$.\n",
    "\n",
    "Let's plot this for different times $t$ for the $f(x) = 0.5 - |x - 0.5|$ from above, using 199 terms in the series:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
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   var self = this;\\n    function AppViewModel() {\\n        for (var key in json_data) {\\n            var el = json_data[key];\\n            this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n        }\\n        \\n        [this[\\\"formatted_val\\\"]=ko.computed(    function(){\\n        return this.formatted_vals()[parseInt(this.index())-(1)];\\n    }\\n,this)]\\n        [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"260932272714199448\\\",\\\"id\\\":\\\"17599371369714419038\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"260932272714199448\\\",\\\"id\\\":\\\"2368971869918299780\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n        \\n    }\\n    self.model = new AppViewModel();\\n    self.valueFromJulia = {};\\n    for (var key in json_data) {\\n        self.valueFromJulia[key] = false;\\n    }\\n    ko.applyBindings(self.model, self.dom);\\n}\\n);\\n    (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/d2675103c724f99cdfcc3549728e088170514311-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/9d05d0c2e7439dab4d690d547fa152c73d9dcd16-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\"],\"observables\":{\"changes\":{\"sync\":false,\"id\":\"17599371369714419038\",\"value\":0},\"index\":{\"sync\":true,\"id\":\"2368971869918299780\",\"value\":1}}},\"children\":[{\"props\":{\"className\":\"interact-flex-row interact-widget\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact-flex-row-left\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact \",\"style\":{\"padding\":\"5px 10px 0px 10px\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"label\"},\"children\":[\"time t\"]}]},{\"props\":{\"className\":\"interact-flex-row-center\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"max\":1001,\"min\":1,\"attributes\":{\"type\":\"range\",\"data-bind\":\"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\",\"orient\":\"horizontal\"},\"step\":1,\"className\":\"slider slider is-fullwidth\",\"style\":{}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"input\"},\"children\":[]}]},{\"props\":{\"className\":\"interact-flex-row-right\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"attributes\":{\"data-bind\":\"text: 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'><\\/img>\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[]}]}}}},\"children\":[{\"props\":{},\"nodeType\":\"ObservableNode\",\"type\":\"node\",\"instanceArgs\":{\"id\":\"15804959645452981788\",\"name\":\"obs-node\"},\"children\":[]}]}]},\n",
       "            window,\n",
       "        );\n",
       "    } else {\n",
       "        document\n",
       "            .querySelector('[data-webio-mountpoint=\"6960191437181364859\"]')\n",
       "            .innerHTML = (\n",
       "                '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb\">' +\n",
       "                '<p><strong>WebIO not detected.</strong></p>' +\n",
       "                '<p>Please read ' +\n",
       "                '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
       "                'for more information on how to resolve this issue.</p>' +\n",
       "                '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
       "                '</div>'\n",
       "            );\n",
       "    }\n",
       "    </script>\n",
       "</div>\n"
      ],
      "text/plain": [
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   var self = this;\\n    function AppViewModel() {\\n        for (var key in json_data) {\\n            var el = json_data[key];\\n            this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n        }\\n        \\n        [this[\\\"formatted_val\\\"]=ko.computed(    function(){\\n        return this.formatted_vals()[parseInt(this.index())-(1)];\\n    }\\n,this)]\\n        [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"260932272714199448\\\",\\\"id\\\":\\\"17599371369714419038\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"260932272714199448\\\",\\\"id\\\":\\\"2368971869918299780\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n        \\n    }\\n    self.model = new AppViewModel();\\n    self.valueFromJulia = {};\\n    for (var key in json_data) {\\n        self.valueFromJulia[key] = false;\\n    }\\n    ko.applyBindings(self.model, self.dom);\\n}\\n);\\n    (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/d2675103c724f99cdfcc3549728e088170514311-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/9d05d0c2e7439dab4d690d547fa152c73d9dcd16-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\")])], Dict{Symbol,Any}(:className => \"field interact-widget\")), Observable{Any} with 0 listeners. Value:\n",
       "Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Figure(PyObject <Figure size 640x480 with 1 Axes>)], Dict{Symbol,Any}(:className => \"interact-flex-row interact-widget\"))], Dict{Symbol,Any}())"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "@webio": {
       "kernelId": "1d906ee0-9117-4cf7-bb86-e93666d2a1a9"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = figure()\n",
    "@manipulate for t in slider(0:0.001:1, value=0.0, label=\"time t\")\n",
    "    withfig(fig) do\n",
    "        b = @. sinecoef(f, 1:199) * exp(-((1:199)*π)^2 * t)\n",
    "        plot(x, [sinesum(b, x) for x in x])\n",
    "        xlabel(L\"x\")\n",
    "        title(\"diffusion solution at time $t\")\n",
    "        ylim(0,0.5)\n",
    "    end\n",
    "end"
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    "Notice that the sharp kink (the slope discontinuity) \"diffuses away\" almost immediately, because that sharp kink is created by the high-frequency sine-series terms that decay very rapidly.  After a short while, in fact, the solution just looks like $\\sin(\\pi x)$, because it is dominated by the $n=1$ term in the series."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving the wave equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have the *wave* equation $\\frac{\\partial^2 u}{\\partial x^2} = \\frac{\\partial^2 u}{\\partial t^2}$, with Dirichlet boundary conditions $u(0,t) = u(1,t) = 0$, and initial conditions $u(x,0) = f(x)$ and $\\dot{u}(x,0) = 0$, we can also solve the equation by expanding $u(x,t)$ in a Fourier sine series.  From class:\n",
    "\n",
    "* $u(x,t) = \\sum_{n=0}^\\infty b_n \\sin(n\\pi x) \\cos{n\\pi t}$\n",
    "\n",
    "where $b_n$ are the sine-series coefficients of the initial condition $f(x)$.\n",
    "\n",
    "Let's again plot this for different times $t$ for the $f(x) = 0.5 - |x - 0.5|$ from above, using 199 terms in the series:"
   ]
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(WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"1669070286673146683\\\",\\\"id\\\":\\\"14165051404786801274\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n        \\n    }\\n    self.model = new AppViewModel();\\n    self.valueFromJulia = {};\\n    for (var key in json_data) {\\n        self.valueFromJulia[key] = false;\\n    }\\n    ko.applyBindings(self.model, self.dom);\\n}\\n);\\n    (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/d2675103c724f99cdfcc3549728e088170514311-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"\\/assetserver\\/9d05d0c2e7439dab4d690d547fa152c73d9dcd16-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\"],\"observables\":{\"changes\":{\"sync\":false,\"id\":\"17930377566971587617\",\"value\":0},\"index\":{\"sync\":true,\"id\":\"14165051404786801274\",\"value\":1}}},\"children\":[{\"props\":{\"className\":\"interact-flex-row interact-widget\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact-flex-row-left\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"className\":\"interact \",\"style\":{\"padding\":\"5px 10px 0px 10px\"}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"label\"},\"children\":[\"time t\"]}]},{\"props\":{\"className\":\"interact-flex-row-center\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"max\":1001,\"min\":1,\"attributes\":{\"type\":\"range\",\"data-bind\":\"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\",\"orient\":\"horizontal\"},\"step\":1,\"className\":\"slider slider is-fullwidth\",\"style\":{}},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"input\"},\"children\":[]}]},{\"props\":{\"className\":\"interact-flex-row-right\"},\"nodeType\":\"DOM\",\"type\":\"node\",\"instanceArgs\":{\"namespace\":\"html\",\"tag\":\"div\"},\"children\":[{\"props\":{\"attributes\":{\"data-bind\":\"text: 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       "            window,\n",
       "        );\n",
       "    } else {\n",
       "        document\n",
       "            .querySelector('[data-webio-mountpoint=\"4703870838943912851\"]')\n",
       "            .innerHTML = (\n",
       "                '<div style=\"padding: 1em; background-color: #f8d6da; border: 1px solid #f5c6cb\">' +\n",
       "                '<p><strong>WebIO not detected.</strong></p>' +\n",
       "                '<p>Please read ' +\n",
       "                '<a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">the troubleshooting guide</a> ' +\n",
       "                'for more information on how to resolve this issue.</p>' +\n",
       "                '<p><a href=\"https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/\" target=\"_blank\">https://juliagizmos.github.io/WebIO.jl/latest/troubleshooting/not-detected/</a></p>' +\n",
       "                '</div>'\n",
       "            );\n",
       "    }\n",
       "    </script>\n",
       "</div>\n"
      ],
      "text/plain": [
       "Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Scope(Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :label), Any[\"time t\"], Dict{Symbol,Any}(:className => \"interact \",:style => Dict{Any,Any}(:padding => \"5px 10px 0px 10px\")))], Dict{Symbol,Any}(:className => \"interact-flex-row-left\")), Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :input), Any[], Dict{Symbol,Any}(:max => 1001,:min => 1,:attributes => Dict{Any,Any}(:type => \"range\",Symbol(\"data-bind\") => \"numericValue: index, valueUpdate: 'input', event: {change: function (){this.changes(this.changes()+1)}}\",\"orient\" => \"horizontal\"),:step => 1,:className => \"slider slider is-fullwidth\",:style => Dict{Any,Any}()))], Dict{Symbol,Any}(:className => \"interact-flex-row-center\")), Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Node{WebIO.DOM}(WebIO.DOM(:html, :p), Any[], Dict{Symbol,Any}(:attributes => Dict(\"data-bind\" => \"text: formatted_val\")))], Dict{Symbol,Any}(:className => \"interact-flex-row-right\"))], Dict{Symbol,Any}(:className => \"interact-flex-row interact-widget\")), Dict{String,Tuple{Observables.AbstractObservable,Union{Nothing, Bool}}}(\"changes\" => (Observable{Int64} with 1 listeners. Value:\n",
       "0, nothing),\"index\" => (Observable{Any} with 2 listeners. Value:\n",
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   var self = this;\\n    function AppViewModel() {\\n        for (var key in json_data) {\\n            var el = json_data[key];\\n            this[key] = Array.isArray(el) ? ko.observableArray(el) : ko.observable(el);\\n        }\\n        \\n        [this[\\\"formatted_val\\\"]=ko.computed(    function(){\\n        return this.formatted_vals()[parseInt(this.index())-(1)];\\n    }\\n,this)]\\n        [this[\\\"changes\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"changes\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"changes\\\",\\\"scope\\\":\\\"1669070286673146683\\\",\\\"id\\\":\\\"17930377566971587617\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"changes\\\"]=false}),self),this[\\\"index\\\"].subscribe((function (val){!(this.valueFromJulia[\\\"index\\\"]) ? (WebIO.setval({\\\"name\\\":\\\"index\\\",\\\"scope\\\":\\\"1669070286673146683\\\",\\\"id\\\":\\\"14165051404786801274\\\",\\\"type\\\":\\\"observable\\\"},val)) : undefined; return this.valueFromJulia[\\\"index\\\"]=false}),self)]\\n        \\n    }\\n    self.model = new AppViewModel();\\n    self.valueFromJulia = {};\\n    for (var key in json_data) {\\n        self.valueFromJulia[key] = false;\\n    }\\n    ko.applyBindings(self.model, self.dom);\\n}\\n);\\n    (WebIO.importBlock({\\\"data\\\":[{\\\"name\\\":\\\"knockout\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/d2675103c724f99cdfcc3549728e088170514311-knockout.js\\\"},{\\\"name\\\":\\\"knockout_punches\\\",\\\"type\\\":\\\"js\\\",\\\"url\\\":\\\"/assetserver/9d05d0c2e7439dab4d690d547fa152c73d9dcd16-knockout_punches.js\\\"}],\\\"type\\\":\\\"async_block\\\"})).then((imports) => handler.apply(this, imports));\\n}\\n\")])], Dict{Symbol,Any}(:className => \"field interact-widget\")), Observable{Any} with 0 listeners. Value:\n",
       "Node{WebIO.DOM}(WebIO.DOM(:html, :div), Any[Figure(PyObject <Figure size 640x480 with 1 Axes>)], Dict{Symbol,Any}(:className => \"interact-flex-row interact-widget\"))], Dict{Symbol,Any}())"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "@webio": {
       "kernelId": "1d906ee0-9117-4cf7-bb86-e93666d2a1a9"
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = figure()\n",
    "@manipulate for t in slider(0:0.01:10, value=0.0, label=\"time t\")\n",
    "    withfig(fig) do\n",
    "        b = @. sinecoef(f, 1:199) * cos(((1:199)*π) * t)\n",
    "        plot(x, [sinesum(b, x) for x in x])\n",
    "        xlabel(L\"x\")\n",
    "        title(\"wave solution at time $t\")\n",
    "        ylim(-0.5,0.5)\n",
    "        grid()\n",
    "    end\n",
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    "Now we have an oscillating wave, which bounced up and down between two triangle shapes.\n",
    "\n",
    "(This may seem unrealistic to you: if you actually stretch a string into a triangle shape and let it go, it doesn't retain the sharp kinks seen here.  That is due to an effect called *dispersion* that we are not including in the wave equation...yet.)"
   ]
  }
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